The sum of consecutive positive integers is 1998. If is odd, what is the greatest possible value for ?Source: mathcontest.olemiss.edu 9/26/2011

SOLUTION
Before tackling this problem we should revisit two formulas related to the sum of consecutive positive integers. Let where is odd be a collection of consecutive positive integers.
For example, is such a collection where

Sum formula
The formula that calculates the sum is given byThe second factor in the above formula really is the number of terms in the collection, so in this problem we have a simpler formulaThe sum in our example